Sampling Distribution + CLT
Review:
A simple simulation:
Many simulations:
Inference: Point Estimates
Review:
Some important estimators
Sample mean: \(\bar{X} = \frac{X_1+ \cdots+ X_n}{n}\)
Sample Variance: \(S^2 = \frac{1}{n-1} \sum_{i= 1}^n (X_i - \bar{X})^2\)
Loops:
n <- 10
N <- 1000
mu <- 105
sigma <- 12
## Create an empty matrix to store the samples in and an empty vector to store sample variances
samples <- matrix(NA, nrow = N, ncol = n)
sample.variances<-rep(NA, N)
for (i in 1:N) {
samples[i,] <- rnorm(n, mean=mu, sd=sigma)
deviation <- samples[i,] - mean(samples[i,])
sample.variances[i] <- (1/(n-1)) * sum((deviation)^2)
}
mean(sample.variances)#> [1] 142.6414
#> [1] 142.0096